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Autonomous and non-autonomous fixed-time leader-follower consensus for second-order multi-agent systems

Miguel A. Trujillo, Rodrigo Aldana-López, David Gomez Gutierrez, Michael Defoort, Javier Ruiz Leon, Hector M. Becerra

TL;DR

This work addresses fixed_time leader_follower consensus for second_order MAS with double_integrator dynamics and partial leader access. It proposes a two_stage design: a distributed fixed_time observer to estimate the leader state, followed by a fixed_time controller to track the leader trajectory, and compares autonomous versus non_autonomous protocols. The autonomous scheme fixes the UBST a priori, while the non_autonomous scheme uses bounded time_varying gains to reduce conservatism and tighten convergence times. Simulation results on a five_agent network validate fixed_time convergence for both observer and controller with improved performance in the non_autonomous design, underscoring the practical viability of precise timing in distributed coordination.

Abstract

This paper addresses the problem of consensus tracking with fixed-time convergence, for leader-follower multi-agent systems with double-integrator dynamics, where only a subset of followers has access to the state of the leader. The control scheme is divided into two steps. The first one is dedicated to the estimation of the leader state by each follower in a distributed way and in a fixed-time. Then, based on the estimate of the leader state, each follower computes its control law to track the leader in a fixed-time. In this paper, two control strategies are investigated and compared to solve the two mentioned steps. The first one is an autonomous protocol which ensures a fixed-time convergence for the observer and for the controller parts where the Upper Bound of the Settling-Time (UBST) is set a priory by the user. Then, the previous strategy is redesigned using time-varying gains to obtain a non-autonomous protocol. This enables to obtain less conservative estimates of the UBST while guaranteeing that the time-varying gains remain bounded. Some numerical examples show the effectiveness of the proposed consensus protocols.

Autonomous and non-autonomous fixed-time leader-follower consensus for second-order multi-agent systems

TL;DR

This work addresses fixed_time leader_follower consensus for second_order MAS with double_integrator dynamics and partial leader access. It proposes a two_stage design: a distributed fixed_time observer to estimate the leader state, followed by a fixed_time controller to track the leader trajectory, and compares autonomous versus non_autonomous protocols. The autonomous scheme fixes the UBST a priori, while the non_autonomous scheme uses bounded time_varying gains to reduce conservatism and tighten convergence times. Simulation results on a five_agent network validate fixed_time convergence for both observer and controller with improved performance in the non_autonomous design, underscoring the practical viability of precise timing in distributed coordination.

Abstract

This paper addresses the problem of consensus tracking with fixed-time convergence, for leader-follower multi-agent systems with double-integrator dynamics, where only a subset of followers has access to the state of the leader. The control scheme is divided into two steps. The first one is dedicated to the estimation of the leader state by each follower in a distributed way and in a fixed-time. Then, based on the estimate of the leader state, each follower computes its control law to track the leader in a fixed-time. In this paper, two control strategies are investigated and compared to solve the two mentioned steps. The first one is an autonomous protocol which ensures a fixed-time convergence for the observer and for the controller parts where the Upper Bound of the Settling-Time (UBST) is set a priory by the user. Then, the previous strategy is redesigned using time-varying gains to obtain a non-autonomous protocol. This enables to obtain less conservative estimates of the UBST while guaranteeing that the time-varying gains remain bounded. Some numerical examples show the effectiveness of the proposed consensus protocols.
Paper Structure (13 sections, 9 theorems, 62 equations, 9 figures, 1 table)

This paper contains 13 sections, 9 theorems, 62 equations, 9 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Graph Theory
  4. On finite-time and fixed-time
  5. Problem statement
  6. Fixed-time leader-follower consensus using autonomous protocols
  7. Distributed fixed-time observer
  8. A Fixed-time tracking controller
  9. Fixed-time leader-follower consensus with improved estimate for the UBST using non-autonomous protocol
  10. Simulation results
  11. Fixed-time leader-follower consensus using autonomous protocols
  12. Fixed-time leader-follower consensus using non-autonomous protocols
  13. Conclusions

Key Result

Lemma 1

Ren2013Ni2010 Let $\hat{\mathcal{X}}$ be the communication graph among all the agents with the leader as the root. Then, matrix $\mathcal{M}(\hat{\mathcal{X}}_{})$ is symmetric positive definite.

Figures (9)

  • Figure 1: Communication topology with 5 followers.
  • Figure 2: Autonomous protocol. Leader states estimation for each agent.
  • Figure 3: Autonomous protocol. Trajectories of each agent.
  • Figure 4: Non-autonomous protocol. Leader states estimation for each agent.
  • Figure 5: Non-autonomous protocol. Trajectories of each agent.
  • ...and 4 more figures

Theorems & Definitions (25)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Lemma 1
  • Definition 5
  • Definition 6
  • Theorem 1
  • Theorem 2
  • Definition 7
  • ...and 15 more